Name Date Class. Write in exponential form

Transcription

1 Name Date Class Chapter 8 Practice 8-1 Exponents Write in exponential form ( 8) ( 8) ( 8) ( 8) b b b b Simplify ( 6) ( 7) 2 9. ( 5) ( 9) ( 4) ( 3) ( 10) ( 14) (16) 2 Evaluate each expression for the given values of the variables. 21. n 3 5 for n x 2 y 3 for x 5 and y m p q 2 for m 5, p 2, and q a 4 2(b c 2 ) for a 2, b 4, and c 1

2 Name Date Class 25. n 3 5p for n 4 and p x 2 y 3 for x 5 and y a b 6 c for a 3, b 4, and c s 4 (t r) 5 for s 2, t 7, and r y x x y xy for x 2 and y x 9 (y z) for x 1, y 10, and z x z y x for x 2, y 4, and z ac b c for a 12, b 6, and c Write an expression for five times a number used as a factor three times.

3 Name Date Class Chapter 8 Practice 8-2 Integer Exponents Simplify Simplify. 13. ( 2) ( 4) ( 9) ( 3) ( 6) 0 4 1

4 Name Date Class 23. 3( 9) ( 5) 2 (4 3) One centimeter equals 10 2 meter. Simplify The area of a square is 10 4 square feet. Simplify Original content Copyright by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor. 14 Holt Mathematics

5 Name Date Class Chapter 8 Practice 8-2B Integer Exponents Simplify Simplify. 13. ( 3) ( 6) ( 6) ( 2) 2

6 Name Date Class ( 19) ( 4) ( 3) 2 (2 4) 0

7 Name Date Class Chapter 8 Lesson 8-1 Problem Solving Exponents Write the correct answer. 1. The formula for the volume of a cube is V e 3 where e is the length of a side of the cube. Find the volume of a cube with side length 6 cm. Solution: V e 3, e 6 V cm 3 2. The distance in feet traveled by a falling object is given by the formula d 16t 2 where t is the time in seconds. Find the distance an object falls in 4 seconds. d 16t 2 d 16 2 d 3. The surface area of a cube can be found using the formula S 6e 2 where e is the length of a side of the cube. Find the surface area of a cube with side length 6 cm. 4. John is paid 2 cents for doing the dishes the first night, 4 cents the second, 8 cents the third, and so on, doubling each night. Write an expression using exponents for the amount John will get paid on the tenth night. Use the table below for Exercises 5 7. It shows the number of s forwarded at each level if each person continues a chain by forwarding an to 10 friends. Choose the letter for the best answer. 5. How many s were forwarded at level 5 alone? 6. How many s were forwarded at level 6 alone? Level Forwarded s s forwarded , , How many total s have been forwarded after 6 levels?

8 Name Date Class Chapter 8 Lesson 8-2 Problem Solving Integer Exponents Write the correct answer. 1. The weight of 10 7 dust particles is 1 gram. Simplify The weight of one dust particle is 10 7 gram. Simplify As of 2001, only 10 6 rural homes in the United States had broadband Internet access. Simplify Atomic clocks measure time in microseconds. A microsecond is 10 6 second. Simplify The diameter of the nucleus of an atom is about meter. Simplify The diameter of the nucleus of an atom is nanometer. How many nanometers is the diameter of the nucleus of an atom? 7. A ruby-throated hummingbird weighs about 3 2 ounce. Simplify A ruby-throated hummingbird breathes times per minute while at rest. Simplify this amount.

9 Chapter 8 Practice 8-3 Properties of Exponents Write the product or quotient as one power. 1. x 10 x 8 2. ( 10) 14 ( 10) 4 3. d 5 d t 12 t 5 6. ( x)10 ( x) ( k) 12 ( k) x 8 x y 12 y ( 11) 20 ( 11) ( a) 6 ( a) ( a)12 ( a) 7 Simplify. 21. (5 3 ) (7 4 ) (2 6 ) (x 2 ) (3 2 ) (12 0 ) (w 4 ) (y 1 ) (9 2 ) (10 0 ) (x 4 ) (5 2 ) 0

10 Write as one power. 33. x 3 x 2 x x 7 x 2 x ( 4) 4 ( 4) 6 ( 4) Justine and ninety-nine of her co-workers won the lottery worth $10 8. They all received their winnings over ten years. How much did each receive in a one-year period? 40. A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number? 41. Jefferson High School has a student body of 6 4 students. Each class has approximately 6 2 students. How many classes does the school have? Write the answer as one power. 42. Write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times. Then, write the product as one power.

11 EJMS Math Name ID: 1 h k2b0j1w7k UKbuMtraA USPomf[tJwEakrmek klnlwcg.t l zatlvlh MrrizgthbtGsd VrFeZsseVrgvjekdW. Practice 8-3B Use shortcuts to simplify. Your answer should contain only positive exponents. 1) ) Date Period 3) ) ) 2 p 2 4 p 6) 2v 2 3v 7) 2x 2x 2 8) 3aa 2 9) ) ) ) R R2b0N1F7_ AKDuotHaz QS]o`fjthwBaCrQeW \LULZCC.v e kaoldlk JrZiagQhPtcsy NrieLsWeNrKvqeDdC.z m tmtatdfes wwliotkhx aimnkfeinnkihtaei ppqrjeb-rallzgyebbkrsax. -1- Worksheet by Kuta Software LLC

12 13) 8b2 5b 2 14) 6n 3 n 4 15) 2n4 4n 3 16) 2v 2 8v 3 17) ) ) ( 2 2 )2 20) ( 3 2 )2 21) (3a) 2 22) n 2 23) ( a 2 )2 24) (2n) 2 d I2x0[1[7] HKIultba` \SYo_fNtgwgakrje_ OLmLtCQ.k P layl]ls \rpiagrhet[sh xriejs`egrhvyehdf.r ^ mmzardde^ GwsiRtAhy TIhngfoikntiCt]eD BPerieD-YA`lCgoeabhrUa^. -2- Worksheet by Kuta Software LLC

13 Chapter 8 Practice 8-4 Scientific Notation Write each number in standard notation

14 Write each number in scientific notation ,000, , ,406,000, ,280,000, ,100,000, Jupiter is about 778,120,000 kilometers from the Sun. Write this number in scientific notation. 35. The E. coli bacterium is about meters wide. A hair is about meters wide. Which is wider, the bacterium or the hair?

15 EJMS Mathematics Name ID: 1 a h2p0v1h7c YKZujtuaD rs[oqfjt^w`a[rxes JLXLHCb.K f favlwly \rvipgihqtnsw yr[e_syekruvle`dm. Practice 8-4B Write each number in scientific notation. 1) ) 0.8 Date Period 3) ) ) ) ) ) ) ) ) ) I o2k0e1t7f ekfuithak asyotf_tewnaorteh `LpLdCZ.h h daslhln DrgiUgchrtHsF hroeqsyeyrqvme\dx.s r rm^akdhec awkint]hv ei\nefxiqn[iitvew jprrmet-bamlogae_borpaz. -1- Worksheet by Kuta Software LLC

16 Write each number in standard notation. 13) ) ) ) ) ) ) ) ) ) ) ) X Q2X0V1j7l FKNugtOaf LSEoJfGtcwhaIr]ed olwlvct.q p nazlqly erlicgthotbsc nrteasje_rpvpeqdx.l I ymaamdney [wtistbhk aiinaflisnaixtueh dpmrxed-[anlxgqepbmrbah. -2- Worksheet by Kuta Software LLC

17 Name Date Class Chapter 8 Lesson 8-3 Problem Solving Properties of Exponents Write each answer as a power. 1. Cindy estimates that there are 2 10 fruit flies in each of 2 2 jars. How many fruit flies are there in all? 2. If an antibiotic kills bacteria at a rate of 8 9 per sec, how many bacteria would be killed after 8 2 sec? 3.A satellite orbits the earth at about 13 4 km per hour. How long would it take to complete 24 orbits, which is a distance of about 13 5 km? 4. The side of a cube is 3 4 centimeters long. What is the volume of the cube? (Hint: V s 3.) Use the table to answer Exercises 5 6. The table describes the number of people involved at each level of a pyramid scheme. In a pyramid scheme, each individual recruits others to participate, who in turn recruit others, and so on. Choose the letter of the best answer. 5. Using exponents, how many people will be involved at level 6? 6. How many times as many people will be involved at level 6 than at level 2? Pyramid Scheme Each person recruits 5 others. Level Total Number of People

18 Name Date Class Chapter 9 Lesson 8-4 Problem Solving Scientific Notation Write the correct answer. 1. A new transistor can switch on and off 1.5 trillion times a second. Express the speed of the transistor in scientific notation. 2. With this transistor, computers will be able to do calculations in the time it takes to blink your eye. Express the number of calculations using standard notation. (Hint: Write 9 zeros) 3. The length of an element in the transistor is times smaller than the width of a human hair. Express in standard notation. Use the table to answer Exercises 5 9. Choose the best answer. 4. Express a light-year in miles using scientific notation. 5. How many miles is it from Earth to the star Sirius? Distance From Earth To Stars Light-Year 5,880,000,000,000 mi Distance Star Constellation (light-years) Sirius Canis Major 8 Canopus Carina 650 Alpha Centauri Cantaurus 4 Vega Lyra How many miles is it from Earth to the star Canopus? 7. How many miles is it from Earth to the star Alpha Centauri?

19 Chapter 8 Practice 8-5 Squares and Square Roots Find the two square roots of each number Simplify each expression ( 144 6)

20 ( 225 9) 32. ( ) 33. The distance from base to base, home plate included, on a baseball field is 90 ft. The bases form a square. What is its area? Switzerland s flag is a square, unlike other flags that are rectangular. 34. Suppose a seamstress is making a flag that has to have an area less than 50 square meters. What is the longest length, to the nearest tenth, the sides can be? (Hint: s A )

21 EJMS Mathematics Name ID: 1 S V2[0Q1n6P mkhuatgaw asiowfktywoa\reej KLNLyCx.v Z BAKl`l^ WrwiIgohutbsl prtebsoewrkvdetdv. Practice 8-6 Estimate each square root. 1) 118 2) 39 Date Period 3) 31 4) 43 5) 2 6) 28 7) 64 8) 67 9) 79 10) 138 c j2u0]1l6b xknurtzap ^SsoNfstKwoaErQeo al\lycc.l b OAIlBlT RrFiDgnhDtjsM brdegscekrav_eldg.b u omkavdven VwjiFt]hz DI[nQfFixnriXtCeH ZPBrceN-qATlvgfeabfrcaz. -1- Worksheet by Kuta Software LLC

22 11) ) 58 13) 86 14) 44 15) 61 16) 4 17) 65 18) 97 19) 68 20) 3 T L2\0t1_6R lkfuftxas BSaotfltQwua[rkew fliljcq.f O NAOlslA creiagyhotqsv KrQeLsvegrIvse[dC.i ` ambazdseu uwrijtqhc vijnxfxiznmictaep JPzrkeG-BAolIgYeVbqrnaN. -2- Worksheet by Kuta Software LLC

23 EJMS Mathematics Name ID: 1 H M2w0M1v7l qkpubt\av MSmoQfhtgwRaorxeh \LvLBCX.x ] JAvlrlF er^isg\hstss` ^reefseekrnvzefd^. Practice 8-6B Estimate each square root. Show work. 1) 123 2) 34 Date Period 3) 120 4) 110 5) 114 6) 142 7) 126 8) 78 9) 50 10) 20 V [2\0j1j7i LKsu`tUaf tstowfbtiwmalreeg BLYLRCi._ G raelzlb vrui[gohkttsn crlevsrehrfvfexdu.d N XM\aldDeZ nwiiztdhb [Iyn_fHienviztMeI YP`r^e[-XAhlAgIe\bUroaK. -1- Worksheet by Kuta Software LLC

24 11) ) ) 60 14) 91 15) ) 64 17) 2 18) 96 19) ) 10 _ t2b0l1u7s kknu^tuai esmotfitqwaalrqew nlwlvck.l b OA`lrle drxikgxh_tzsf lrqelscehrev[eddm.v Q vmuaidke] [wsistqh\ KIonef_iangiwtBeZ ]POrsew-uAalPgGeIbvrDay. -2- Worksheet by Kuta Software LLC

25 Name Date Class Chapter 8 Lesson 8-5 Problem Solving Squares and Square Roots Write the correct answer. 1. For college wrestling competitions, the NCAA requires that the wrestling mat be a square with an area of 1764 square feet. What is the length of each side of the wrestling mat? 2. For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet. What is the length of each side of the wrestling mat? 3. The Japanese art of origami requires folding square pieces of paper. Elena begins with a large sheet of square paper that is 169 square inches. How many squares can she cut out of the paper that are 4 inches on each side? 4. When the James family moved into a new house they had a square area rug that was 132 square feet. In their new house, there are three bedrooms. Bedroom one is 11 feet by 11 feet. Bedroom two is 10 feet by 12 feet and bedroom three is 13 feet by 13 feet. In which bedroom will the rug fit? 5. A square picture frame measures 36 inches on each side. The actual wood trim is 2 inches wide. The photograph in the frame is surrounded by a bronze mat that measures 5 inches. What is the maximum area of the photograph? 6. To create a square patchwork quilt wall hanging, square pieces of material are sewn together to form a larger square. Which is the least number of smaller squares that can be used to create a square patchwork quilt wall hanging? 7. A can of paint claims that one can will cover 400 square feet. If you painted a square with the can of paint, how long would it be on each side? 8. A box of tile contains 12 square tiles. If you tile the largest possible square area using whole tiles, how many tiles will you have left from the box?

26 Name Date Class Chapter 8 Lesson 8-6 Problem Solving Estimating Square Roots The distance to the horizon can be found using the formula d h where d is the distance in kilometers and h is the number of kilometers from the ground. Round your answer to the nearest kilometer. 1. How far is it to the horizon when you are standing on the top of Mt. Everest, a height of 8.85 km? 2. Find the distance to the horizon from the top of Mt. McKinley, Alaska, a height of km. 3. How far is it to the horizon if you are standing on the ground and your eyes are 2 m above the ground? 4. Mauna Kea Hawaii is about 4 km tall. You should be able to see the top of Mauna Kea when you are how far away? You can find the approximate speed of a vehicle that leaves skid marks before it stops. The formulas S L and S L, where S is the speed in miles per hour and L is the length of the skid marks in feet, will give the minimum and maximum speeds that the vehicle was traveling before the brakes were applied. Round to the nearest mile per hour. 5. A vehicle leaves a skid mark of 40 feet before stopping. What was the approximate speed of the vehicle before it stopped? 6. A vehicle leaves a skid mark of 200 feet before stopping. What was the approximate speed of the vehicle before it stopped?

27 EJMS Mathematics Name ID: 1 r f2q0e1i6v gkyuhtcae NS\oifvtdwOaGrJey xlllzcw.t F xajlvlr xrtikg[hftssw LrRehsYeTrLvKeUdg. Practice 8-7 Simplify each radical, if possible. 1) 82 2) 116 Date Period 3) 49 4) 39 5) 141 6) 5 7) 124 8) 136 9) 34 10) 73 S s2y0^1f6u AKFuWtfaX hsdosfytewmatrtey ^LOLBCa.N k AAdlwlG FrDiZgyh]tjsq TrCeusieQrEvDeYdx.H \ MMvaXdZet \wtixtohh viinefridnfi[teec hp]rpe[-[aplbgserbirzaz. -1- Worksheet by Kuta Software LLC

28 11) ) 45 13) ) 27 15) 12 16) 43 17) 76 18) 80 19) ) 53 Z U2P0Y1Y6\ YKEuQtOaH TSzoJfOtJwxaBrveS blplkcf.` N daslcle LrfiFgwhBtjsG Rr[elsfeKrLv^eWdT.a r [MeaNdIeF ZwEiktNhY IIrnYftiOnJimtEek dpnrven-maml`gpezbdrqaj. -2- Worksheet by Kuta Software LLC

29 EJMS Mathematics Name ID: 1 Q z2r0t1e7k AKLuetiaw ESUoFfotlwbaprLeD ILYLJCk.t ` danlylu ircibgbhstnsh drvehsoe\rrvceddz. Practice 8-7B Simplify each radical, if possible. 1) 106 2) 103 Date Period 3) 14 4) 121 5) 90 6) 127 7) 6 8) 42 9) ) 68 d Q2X0L1H7` \KJuQtEaC rseobfutswgatrieg CL_L_CN.x g zaplolq WrtiXgyh^tUsx ArUews^eZrBvNegdZ.r c XMwaZdSep ]wiiut_hv CIPnmfSiIngiStBek eperreg-hahlbgbewbirqaj. -1- Worksheet by Kuta Software LLC

30 11) 44 12) 84 13) ) 33 15) 97 16) 60 17) 88 18) 9 19) ) 120 c [2H0m1x7Q HKiuetZav LSVoTfZtZwharrCeL hlklcci.z t WAGlQl] zrripghhntasf grje_sye_rxvoe\dg.w N ^MFaDd]eJ xwaittyhh wiznrfdignliptbex uptrmei-_apl_gmebbrrlaw. -2- Worksheet by Kuta Software LLC

31 Simplifying Radicals Maze Name start